Particle-based Bayesian deep learning often requires a similarity metric to compare two networks. However, naive similarity metrics lack permutation invariance and are inappropriate for comparing networks. Centered Kernel Alignment (CKA) on feature kernels has been proposed to compare deep networks but has not been used as an optimization objective in Bayesian deep learning. In this paper, we explore the use of CKA in Bayesian deep learning to generate diverse ensembles and hypernetworks that output a network posterior. Noting that CKA projects kernels onto a unit hypersphere and that directly optimizing the CKA objective leads to diminishing gradients when two networks are very similar. We propose adopting the approach of hyperspherical energy (HE) on top of CKA kernels to address this drawback and improve training stability. Additionally, by leveraging CKA-based feature kernels, we derive feature repulsive terms applied to synthetically generated outlier examples. Experiments on both diverse ensembles and hypernetworks show that our approach significantly outperforms baselines in terms of uncertainty quantification in both synthetic and realistic outlier detection tasks.

Bayesian neural networks (BNNs) provide a formalism to quantify and calibrate uncertainty in deep learning. Current inference approaches for BNNs often resort to few-sample estimation for scalability, which can harm predictive performance, while its alternatives tend to be computationally prohibitively expensive. We tackle this challenge by revealing a previously unseen connection between inference on BNNs and volume computation problems. With this observation, we introduce a novel collapsed inference scheme that performs Bayesian model averaging using collapsed samples. It improves over a Monte-Carlo sample by limiting sampling to a subset of the network weights while pairing it with some closed-form conditional distribution over the rest. A collapsed sample represents uncountably many models drawn from the approximate posterior and thus yields higher sample efficiency. Further, we show that the marginalization of a collapsed sample can be solved analytically and efficiently despite the non-linearity of neural networks by leveraging existing volume computation solvers. Our proposed use of collapsed samples achieves a balance between scalability and accuracy. On various regression and classification tasks, our collapsed Bayesian deep learning approach demonstrates significant improvements over existing methods and sets a new state of the art in terms of uncertainty estimation as well as predictive performance.

Bayesian deep learning (BDL) is a promising approach to achieve well-calibrated predictions on distribution-shifted data. Nevertheless, there exists no large-scale survey that evaluates recent SOTA methods on diverse, realistic, and challenging benchmark tasks in a systematic manner. To provide a clear picture of the current state of BDL research, we evaluate modern BDL algorithms on real-world datasets from the WILDS collection containing challenging classification and regression tasks, with a focus on generalization capability and calibration under distribution shift. We compare the algorithms on a wide range of large, convolutional and transformer-based neural network architectures. In particular, we investigate a signed version of the expected calibration error that reveals whether the methods are over-or underconfident, providing further insight into the behavior of the methods. Further, we provide the first systematic evaluation of BDL for fine-tuning large pre-trained models, where training from scratch is prohibitively expensive. Finally, given the recent success of Deep Ensembles, we extend popular single-mode posterior approximations to multiple modes by the use of ensembles. While we find that ensembling single-mode approximations generally improves the generalization capability and calibration of the models by a significant margin, we also identify a failure mode of ensembles when finetuning large transformer-based language models. In this setting, variational inference based approaches such as last-layer Bayes By Backprop outperform other methods in terms of accuracy by a large margin, while modern approximate inference algorithms such as SWAG achieve the best calibration.

Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference offers the tools to tackle this challenge in a scalable way and with some degree of flexibility on the approximation, but for overparameterized models this is challenging due to the over-regularization property of the variational objective. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random matrices, this paper proposes Walsh-Hadamard Variational Inference (WHVI), which uses Walsh-Hadamardbased factorization strategies to reduce the parameterization and accelerate computations, thus avoiding over-regularization issues with the variational objective. Extensive theoretical and empirical analyses demonstrate that WHVI yields considerable speedups and model reductions compared to other techniques to carry out approximate inference for over-parameterized models, and ultimately show how advances in kernel methods can be translated into advances in approximate Bayesian inference for Deep Learning.

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead. We also investigate the prior over functions implied by a vague distribution over neural network weights, explaining the generalization properties of such models from a probabilistic perspective. From this perspective, we explain results that have been presented as mysterious and distinct to neural network generalization, such as the ability to fit images with random labels, and show that these results can be reproduced with Gaussian processes. We also show that Bayesian model averaging alleviates double descent, resulting in monotonic performance improvements with increased flexibility.

There are two major types of uncertainty one can model.

Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approximation of the covariance matrix despite the fact that these matrices are known to give poor uncertainty estimates. To address this issue, we propose a new stochastic, low-rank, approximate natural-gradient (SLANG) method for variational inference in large deep models. Our method estimates a "diagonal plus low-rank" structure based solely on back-propagated gradients of the network log-likelihood. This requires strictly less gradient computations than methods that compute the gradient of the whole variational objective. Empirical evaluations on standard benchmarks confirm that SLANG enables faster and more accurate estimation of uncertainty than mean-field methods, and performs comparably to state-of-the-art methods.